ELEMENTS

OF

The Gift of Dr. Thoncas
of Froserisheir in the County

To 1554

FIRST SIX, AND THE ELEVENTH AND
TWELFTH BOOKS

OF

EUCLI D.

By JOHN BONNY CASTLE,

OF THE ROYAL MILITARY ACADEMY, WOOLWICH.

THE THIRD EDITION.

ساء

LONDON:

PRINTED FOR J. JOHNSON, NO. 72, ST. PAUL'S

CHURCH-YARD,

BY BYE AND LAW, ST. JOHN'S-SQUARE, CLERKENWELL.

Of all the works of antiquity which have been tranfmitted to the prefent times, none are more univerfally and defervedly esteemed than the Elements of Geometry which go' under the name of EUCLID. In many other branches of fcience the moderns have far furpaffed their mafters; but, after a lapse of more than two thousand years, this per formance still maintains its original preeminence, and has even acquired additional celebrity from the fruitless attempts which have been made to establish a different fyftem.

It is, however, generally allowed, that the Elements, as they now ftand, are attended with many difficulties, which greatly retard the progrefs of learners, on their firft entrance upon this ftudy, and prevent them from applying to other branches of knowledge, which, in the prefent advanced state of the fciences, are equally ufeful and im portant. Among other obftacles of this kind A 2

may